Data Set Summary

  • Total Number of Stations = 10451

  • Starting in 2000 and continuing through 2018

  • Total Sapidus Caught was 5531

  • Overall Frequency of Occurrence was 16.1228591

Factor Summaries

Yearly Summaries

Overall Mean Catch Crabs/Hectare: 0.199

Stations with no catch: 8766 / 10451 Stations or 83.88%

Survey_Year Stations Missing Obs % Occurrence Mean Catch SD Overdispersed
2000 497 0 0.1247485 0.1430723 0.7418709 yes
2001 423 0 0.1560284 0.3999519 2.5068184 yes
2002 516 0 0.2151163 0.3052766 1.4236905 yes
2003 486 0 0.2098765 0.3210508 1.2982149 yes
2004 445 0 0.1842697 0.2669802 1.1315465 yes
2005 431 0 0.3039443 0.7309055 4.4504559 yes
2006 398 0 0.2512563 0.2974087 1.2510404 yes
2007 403 0 0.2431762 0.3695068 2.1259831 yes
2008 598 0 0.1505017 0.0887166 0.2906761 no
2009 983 0 0.1576806 0.1372921 0.5387720 yes
2010 700 0 0.1571429 0.1408543 0.5082154 yes
2011 549 0 0.2021858 0.2321763 0.8469300 yes
2012 589 0 0.0916808 0.0595966 0.2344135 no
2013 506 0 0.0790514 0.0494838 0.2574674 yes
2014 685 0 0.1138686 0.1251746 1.2178975 yes
2015 700 0 0.1314286 0.1177831 0.5375021 yes
2016 548 0 0.1423358 0.1173202 0.4557866 yes
2017 603 0 0.1293532 0.1521905 0.6661890 yes
2018 391 0 0.1202046 0.0789907 0.3358133 yes

Yearly Catch Plot

Yearly Frequency of Occurrence

Yearly Side-by

Stat Zone Summaries

StatZone Stations Missing Obs % Occurrence Mean Catch SD Overdispersed
1 5 0 0.0000000 0.0000000 0.0000000 no
2 125 0 0.0160000 0.0047240 0.0371959 no
3 399 0 0.0100251 0.0028436 0.0283030 no
4 443 0 0.0067720 0.0037170 0.0492515 no
5 416 0 0.0072115 0.0026857 0.0333903 no
6 415 0 0.0000000 0.0000000 0.0000000 no
7 253 0 0.0118577 0.0044019 0.0423148 no
8 281 0 0.0533808 0.0596740 0.3968039 yes
9 199 0 0.0000000 0.0000000 0.0000000 no
10 190 0 0.0421053 0.0143626 0.0695699 no
11 1106 0 0.1672694 0.1723934 0.8055450 yes
12 55 0 0.1454545 0.1419970 0.4399969 yes
13 396 0 0.4065657 0.9149865 2.7089809 yes
14 724 0 0.2997238 0.3343395 1.1222703 yes
15 732 0 0.2786885 0.5402363 3.5939280 yes
16 810 0 0.2197531 0.2461144 1.1254532 yes
17 914 0 0.1991247 0.1726239 0.5750543 yes
18 769 0 0.2028609 0.1800542 0.6481025 yes
19 772 0 0.2059585 0.1991595 1.2096515 yes
20 783 0 0.1558110 0.1569738 1.2266493 yes
21 663 0 0.1131222 0.1336667 1.0744834 yes

Stat Zone Catch Plot

Stat Zone Frequency of Occurrence

Stat Zone Side-by

Region Summary

region Stations Missing Obs % Occurrence Mean Catch SD Overdispersed
Texas 2987 0 0.1714094 0.1686456 1.0660434 yes
Louisiana 3577 0 0.2633492 0.3793627 2.0320024 yes
MS Bight 1351 0 0.1487787 0.1489310 0.7365881 yes
Florida 2536 0 0.0118297 0.0088214 0.1367223 yes

Regional Catch Plot

Regional Frequency of Occurrence

Regional Side-by

Region - Season

region Season Stations Missing Obs % Occurrence Mean Catch SD Overdispersed
Texas Summer 1559 0 0.2373316 0.2236771 0.9768701 yes
Texas Fall 1428 0 0.0994398 0.1085657 1.1529185 yes
Louisiana Summer 1855 0 0.3347709 0.5529719 2.6690359 yes
Louisiana Fall 1722 0 0.1864111 0.1923446 0.9153126 yes
MS Bight Summer 695 0 0.1899281 0.2180501 0.9777604 yes
MS Bight Fall 656 0 0.1051829 0.0757027 0.3080248 yes
Florida Summer 1570 0 0.0159236 0.0133319 0.1728732 yes
Florida Fall 966 0 0.0051760 0.0014906 0.0206892 no

Region - Season Catch

Region - Season FOO

Region - Season Side-by

Seasonal Summary

Survey_Year Season Stations Missing Obs % Occurrence Mean Catch SD Overdispersed
2000 Summer 251 0 0.1872510 0.2421858 1.0033596 yes
2000 Fall 246 0 0.0609756 0.0419443 0.2580981 yes
2001 Summer 172 0 0.2383721 0.9058880 3.8750995 yes
2001 Fall 251 0 0.0996016 0.0532547 0.1990548 no
2002 Summer 258 0 0.2829457 0.4726460 1.9025609 yes
2002 Fall 258 0 0.1472868 0.1379073 0.6210433 yes
2003 Summer 206 0 0.3543689 0.4785203 1.2481802 yes
2003 Fall 280 0 0.1035714 0.2051983 1.3240994 yes
2004 Summer 252 0 0.2301587 0.3461199 1.3364643 yes
2004 Fall 193 0 0.1243523 0.1636476 0.7790789 yes
2005 Summer 179 0 0.3240223 1.2656170 6.6823714 yes
2005 Fall 252 0 0.2896825 0.3510905 1.3841155 yes
2006 Summer 235 0 0.3446809 0.4610205 1.5999632 yes
2006 Fall 163 0 0.1165644 0.0615268 0.2074697 no
2007 Summer 179 0 0.2793296 0.2644754 0.7826726 yes
2007 Fall 224 0 0.2142857 0.4534382 2.7645823 yes
2008 Summer 288 0 0.1250000 0.0768972 0.2739921 no
2008 Fall 310 0 0.1741935 0.0996972 0.3053934 no
2009 Summer 539 0 0.2393321 0.2250547 0.7041287 yes
2009 Fall 444 0 0.0585586 0.0307515 0.1434819 no
2010 Summer 386 0 0.2020725 0.2032538 0.6373493 yes
2010 Fall 314 0 0.1019108 0.0641468 0.2577660 yes
2011 Summer 329 0 0.2401216 0.2478884 0.6765975 yes
2011 Fall 220 0 0.1454545 0.2086794 1.0527617 yes
2012 Summer 391 0 0.1023018 0.0670658 0.2382140 no
2012 Fall 198 0 0.0707071 0.0448467 0.2265906 yes
2013 Summer 313 0 0.1118211 0.0704450 0.3082615 yes
2013 Fall 193 0 0.0259067 0.0154898 0.1343925 yes
2014 Summer 364 0 0.1236264 0.1727832 1.6472389 yes
2014 Fall 321 0 0.1028037 0.0711885 0.2949376 yes
2015 Summer 377 0 0.1803714 0.1644393 0.5735665 yes
2015 Fall 323 0 0.0743034 0.0633268 0.4873321 yes
2016 Summer 354 0 0.1638418 0.1475319 0.5221085 yes
2016 Fall 194 0 0.1030928 0.0621916 0.2923462 yes
2017 Summer 322 0 0.1987578 0.2661089 0.8896509 yes
2017 Fall 281 0 0.0498221 0.0216505 0.1216030 no
2018 Summer 284 0 0.1232394 0.0910192 0.3813359 yes
2018 Fall 107 0 0.1121495 0.0470648 0.1589276 no

Seasonal Catch Plot

Seasonal Frequency of Occurrence

Seasonal Side-by

East-West Models

Model A. 2000-2018

This model uses crabs per hectare as the response over the period of 18 years (2000-2018). Data is limited to statzones that were consistently sampled over the time period (i.e. West of Mobile Bay).

Model is a generalized linear model with a negative binomial error distribution. Blue crab catch is predicted as the sum of linear predictors for the year and season when the station was sampled in addition to the region in which it took place, with an interaction between survey year and region. An offset of area towed in hectares was used to predict catch as a rate and account for differences in sampling effort at different stations.

Interaction Plot

Looking at an interaction plot indicates that the impact of each region is not consistent across years and that there is an important interaction in the data.

Model Summary

Understanding p-values in glm model summary. Using the default settings in R sets the contrast levels for factors such that all factors are contrasted against the first/lowest factor level.

For example in our model year is modeled as a factor, which adjusts the intercept for the model for each. The first year is 2000, so all other years are contrasted against that year’s mean estimate. One quick way to confirm what factor level is the contrast is y checking which levels are absent from the summary table summary(my_model)

Contrasts:
year = 2000
region = texas
season = summer

P-values on factor levels in these tables indicate significant deviation from the contrasts. Post-hoc tests are necessary to compare individual levels against one another.

term estimate std.error statistic p.value signif.
(Intercept) -2.6733145 0.2861883 -9.3411033 0.0000000 *
year_f2001 1.0514664 0.3885198 2.7063389 0.0068030 *
year_f2002 1.1109845 0.3641262 3.0510975 0.0022801 *
year_f2003 1.6181556 0.3560574 4.5446484 0.0000055 *
year_f2004 0.6019168 0.3800132 1.5839367 0.1132081
year_f2005 0.7490335 0.3767514 1.9881373 0.0467965 *
year_f2006 0.9665631 0.3737927 2.5858266 0.0097146 *
year_f2007 3.2133377 0.3577372 8.9823978 0.0000000 *
year_f2008 0.5411915 0.3862421 1.4011717 0.1611627
year_f2009 0.4107633 0.3550392 1.1569522 0.2472919
year_f2010 1.3448689 0.3594471 3.7414936 0.0001829 *
year_f2011 1.9049743 0.3591069 5.3047558 0.0000001 *
year_f2012 0.3831549 0.4033193 0.9500038 0.3421103
year_f2013 -0.7583901 0.5169107 -1.4671588 0.1423329
year_f2014 1.7883269 0.3715749 4.8128305 0.0000015 *
year_f2015 1.4152758 0.3734316 3.7899204 0.0001507 *
year_f2016 1.8209074 0.3783259 4.8130653 0.0000015 *
year_f2017 1.3163765 0.3764208 3.4970878 0.0004704 *
year_f2018 0.6150347 0.4944077 1.2439828 0.2135059
regionLouisiana 1.3025000 0.3484004 3.7385142 0.0001851 *
regionMS Bight 0.8634275 0.4531161 1.9055327 0.0567109
seasonFall -1.1944466 0.0705304 -16.9352084 0.0000000 *
year_f2001:regionLouisiana 0.1648747 0.4780710 0.3448749 0.7301884
year_f2002:regionLouisiana 0.0257097 0.4510884 0.0569948 0.9545493
year_f2003:regionLouisiana -0.1879177 0.4552947 -0.4127387 0.6797981
year_f2004:regionLouisiana 0.4723590 0.4684591 1.0083250 0.3132985
year_f2005:regionLouisiana 1.3939977 0.4643367 3.0021269 0.0026810 *
year_f2006:regionLouisiana -0.4545761 0.4857255 -0.9358702 0.3493400
year_f2007:regionLouisiana -2.7262074 0.4554546 -5.9856840 0.0000000 *
year_f2008:regionLouisiana -0.3052659 0.4713490 -0.6476431 0.5172158
year_f2009:regionLouisiana -0.3030983 0.4413966 -0.6866801 0.4922844
year_f2010:regionLouisiana -0.8449438 0.4556076 -1.8545429 0.0636615
year_f2011:regionLouisiana -0.7890426 0.4562994 -1.7292214 0.0837695
year_f2012:regionLouisiana -0.6385626 0.5102218 -1.2515391 0.2107378
year_f2013:regionLouisiana 0.3367814 0.6155953 0.5470824 0.5843221
year_f2014:regionLouisiana -1.3525118 0.4725849 -2.8619450 0.0042105 *
year_f2015:regionLouisiana -0.8975941 0.4738916 -1.8940917 0.0582128
year_f2016:regionLouisiana -1.9674137 0.4845665 -4.0601522 0.0000490 *
year_f2017:regionLouisiana -0.8602303 0.4816509 -1.7860038 0.0740986
year_f2018:regionLouisiana -0.3483886 0.6155945 -0.5659385 0.5714356
year_f2001:regionMS Bight -2.0061988 0.7065977 -2.8392375 0.0045221 *
year_f2002:regionMS Bight -1.2985357 0.6222816 -2.0867334 0.0369122 *
year_f2003:regionMS Bight -1.4933779 0.5899080 -2.5315438 0.0113562 *
year_f2004:regionMS Bight -1.4073476 0.7022656 -2.0040104 0.0450689 *
year_f2005:regionMS Bight 0.8046973 0.6279722 1.2814219 0.2000455
year_f2006:regionMS Bight 0.2127872 0.5937276 0.3583920 0.7200500
year_f2007:regionMS Bight -2.2032994 0.6443902 -3.4192007 0.0006281 *
year_f2008:regionMS Bight -1.5333500 0.6880442 -2.2285633 0.0258430 *
year_f2009:regionMS Bight 0.5905799 0.5645326 1.0461396 0.2954966
year_f2010:regionMS Bight -0.7871644 0.7324190 -1.0747460 0.2824884
year_f2011:regionMS Bight -2.2660645 0.7769977 -2.9164365 0.0035405 *
year_f2012:regionMS Bight -0.5864040 0.8119086 -0.7222538 0.4701385
year_f2013:regionMS Bight 0.5491646 0.9030651 0.6081119 0.5431133
year_f2014:regionMS Bight -1.6589276 0.7381092 -2.2475367 0.0246057 *
year_f2015:regionMS Bight -2.5392383 0.8707171 -2.9162611 0.0035425 *
year_f2016:regionMS Bight -4.0973731 1.2419539 -3.2991346 0.0009698 *
year_f2017:regionMS Bight -0.6909230 0.7147056 -0.9667240 0.3336820
year_f2018:regionMS Bight -0.5752396 0.9424485 -0.6103671 0.5416187

Deviance

null.deviance df.null logLik AIC BIC deviance df.residual
4729.793 7668 -6694.188 13506.38 13916.13 3876.933 7611

Goodness of fit for generalized linear models is described using deviance. A glm will report 2 deviance measures:

null.deviance is the residual variation remaining from the null model. The null model here is the grand mean of blue crab catch per hectare of all observations

deviance is the residual variation remaining from the fitted model. Numbers closer to the null.deviance indicate that the model did not perform much better than the null model.

% deviance explained is calculated as \(\frac{null.deviance - deviance}{null.deviance} * 100\) and expresses the improvement of the fitted model over the null in % deviance explained.

Percent Deviance for model A. = 0.1803166

Likelihood Ratio Test

Significance of the entire factor can be obtained by using a Chi-squared likelihood ratio test.

Predictor Df Deviance AIC LRT Pr(>Chi)
NA 3876.933 13504.38 NA NA
year_f 18 4110.423 13701.87 233.49003 0.0000000
region 2 3890.379 13513.82 13.44667 0.0012025
year_f:region 36 4101.267 13656.71 224.33463 0.0000000

CPUE Timeline

Because we used area towed in the model as an offset predictions from our model can be interprated as crabs per hectare.

Observed vs. Predicted

Model prediction (black) & observed mean values (blue)

Model B. 2009-2018

This model uses crabs per hectare as the response over the period of 9 years (2009-2018). Data selection and sampling effort was consistent over this period. Additionally the survey expanded to the Eastern Gulf of Mexico so stat zones in that region are included as well.

Model is a generalized linear model with a negative binomial error distribution. Blue crab catch is predicted as the sum of linear predictors for the year and season when the station was sampled in addition to the region in which it took place, with an interaction between survey year and region. An offset of area towed in hectares was used to predict catch as a rate and account for differences in sampling effort at different stations.

Interaction Plot

Looking at an interaction plot indicates that the impact of each region is not consistent across years and that there is an important interaction in the data. The sharp peaks for Florida’s linear predictor reflect years when there was no catch.

Model Summary

term estimate std.error statistic p.value signif.
(Intercept) -2.2365366 2.067740e-01 -10.8163341 0.0000000 *
year_f2010 0.9327593 2.919770e-01 3.1946332 0.0014001 *
year_f2011 1.5017278 2.908812e-01 5.1626849 0.0000002 *
year_f2012 -0.0360237 3.428666e-01 -0.1050662 0.9163233
year_f2013 -1.1799056 4.695853e-01 -2.5126542 0.0119827 *
year_f2014 1.3797400 3.047361e-01 4.5276558 0.0000060 *
year_f2015 1.0094688 3.072697e-01 3.2852861 0.0010188 *
year_f2016 1.4121864 3.117953e-01 4.5292099 0.0000059 *
year_f2017 0.9054476 3.109851e-01 2.9115463 0.0035964 *
year_f2018 0.1784394 4.367306e-01 0.4085800 0.6828479
regionLouisiana 0.9938844 2.604943e-01 3.8153789 0.0001360 *
regionMS Bight 1.1850534 3.016999e-01 3.9279207 0.0000857 *
regionFlorida -3.1051374 6.390040e-01 -4.8593399 0.0000012 *
seasonFall -1.2678351 9.489630e-02 -13.3602144 0.0000000 *
year_f2010:regionLouisiana -0.5304500 3.819282e-01 -1.3888736 0.1648712
year_f2011:regionLouisiana -0.4733305 3.815818e-01 -1.2404432 0.2148115
year_f2012:regionLouisiana -0.3245976 4.431647e-01 -0.7324536 0.4638917
year_f2013:regionLouisiana 0.6498545 5.586839e-01 1.1631880 0.2447532
year_f2014:regionLouisiana -1.0345131 3.996120e-01 -2.5887935 0.0096313 *
year_f2015:regionLouisiana -0.5877309 4.012382e-01 -1.4647932 0.1429774
year_f2016:regionLouisiana -1.6644446 4.127629e-01 -4.0324475 0.0000552 *
year_f2017:regionLouisiana -0.5567964 4.100412e-01 -1.3579035 0.1744943
year_f2018:regionLouisiana -0.0201145 5.488016e-01 -0.0366517 0.9707628
year_f2010:regionMS Bight -1.5893384 5.405180e-01 -2.9403987 0.0032779 *
year_f2011:regionMS Bight -2.8589086 6.214104e-01 -4.6006775 0.0000042 *
year_f2012:regionMS Bight -0.8863818 6.369183e-01 -1.3916726 0.1640216
year_f2013:regionMS Bight -0.0560339 7.511082e-01 -0.0746016 0.9405317
year_f2014:regionMS Bight -2.2954727 5.915182e-01 -3.8806457 0.0001042 *
year_f2015:regionMS Bight -3.2553797 7.383571e-01 -4.4089504 0.0000104 *
year_f2016:regionMS Bight -4.8430972 1.143874e+00 -4.2339435 0.0000230 *
year_f2017:regionMS Bight -1.4097640 5.574585e-01 -2.5289129 0.0114416 *
year_f2018:regionMS Bight -1.3784774 7.625142e-01 -1.8078056 0.0706368
year_f2010:regionFlorida -1.2931811 9.800153e-01 -1.3195519 0.1869847
year_f2011:regionFlorida -1.2502857 9.088825e-01 -1.3756297 0.1689363
year_f2012:regionFlorida -24.8886629 8.605019e+04 -0.0002892 0.9997692
year_f2013:regionFlorida 2.6234020 8.394040e-01 3.1253150 0.0017761 *
year_f2014:regionFlorida -0.6072040 7.811682e-01 -0.7773025 0.4369803
year_f2015:regionFlorida 1.1462852 7.169613e-01 1.5988103 0.1098628
year_f2016:regionFlorida -26.2510380 9.093251e+04 -0.0002887 0.9997697
year_f2017:regionFlorida 0.0346248 7.968898e-01 0.0434499 0.9653429
year_f2018:regionFlorida 1.0195593 8.329089e-01 1.2240947 0.2209165

Deviance

null.deviance df.null logLik AIC BIC deviance df.residual
3412.127 6230 -3424.967 6933.935 7216.901 2183.195 6190

Goodness of fit for generalized linear models is described using deviance. A glm will report 2 deviance measures:

null.deviance is the residual variation remaining from the null model. The null model here is the grand mean of blue crab catch per hectare of all observations

deviance is the residual variation remaining from the fitted model. Numbers closer to the null.deviance indicate that the model did not perform much better than the null model.

% deviance explained is calculated as \(\frac{null.deviance - deviance}{null.deviance} * 100\) and expresses the improvement of the fitted model over the null in % deviance explained.

Percent Deviance for model B. = 0.3601659

Likelihood Ratio Test

Predictor Df Deviance AIC LRT Pr(>Chi)
NA 2183.195 6931.935 NA NA
year_f 9 2261.870 6992.609 78.67436 0
region 3 2295.875 7038.615 112.68032 0
year_f:region 27 2327.365 7022.105 144.17031 0

CPUE Timeline

Because we used area towed in the model as an offset predictions from our model can be interprated as crabs per hectare.

Observed vs. Predicted

Model prediction (black) & observed mean values (blue)

Manuscript Model

Model Dataset

The following numbers are from the Western Gulf Dataset used in the generalized linear model*

  • Total Number of Stations = 7669

  • Starting in 2000 and continuing through 2018

  • Total Sapidus Caught was 5430

  • Overall Frequency of Occurrence was 21.3717564

  • Overall Mean Catch Crabs/Hectare:** 0.267

  • Stations with no catch:** 6030 / 7669 Stations or 78.63%

Yearly Catch Plot

NOTE: Contains Data Across All Years and Regions (Including Florida)

Survey Year Stations Missing Obs % Occurrence Mean Catch SD Overdispersed
2000 491 0 0.1242363 0.1434330 0.7458628 yes
2001 416 0 0.1586538 0.4066819 2.5273291 yes
2002 514 0 0.2159533 0.3064645 1.4263351 yes
2003 478 0 0.2112971 0.3253341 1.3084392 yes
2004 440 0 0.1863636 0.2700141 1.1376114 yes
2005 430 0 0.3046512 0.7326053 4.4554998 yes
2006 393 0 0.2468193 0.2933579 1.2552633 yes
2007 401 0 0.2443890 0.3713497 2.1311305 yes
2008 596 0 0.1510067 0.0890143 0.2911187 no
2009 975 0 0.1569231 0.1354986 0.5365246 yes
2010 699 0 0.1573677 0.1410559 0.5085514 yes
2011 549 0 0.2021858 0.2321763 0.8469300 yes
2012 589 0 0.0916808 0.0595966 0.2344135 no
2013 503 0 0.0795229 0.0497789 0.2582070 yes
2014 684 0 0.1125731 0.1243615 1.2186026 yes
2015 696 0 0.1321839 0.1184600 0.5389722 yes
2016 547 0 0.1425960 0.1175347 0.4561761 yes
2017 603 0 0.1293532 0.1521905 0.6661890 yes
2018 391 0 0.1202046 0.0789907 0.3358133 yes

Region - Season Plot

NOTE: Zeros removed for plotting

Region Season Stations Missing Obs % Occurrence Mean Catch SD Overdispersed
Texas Summer 1559 0 0.2373316 0.2236771 0.9768701 yes
Texas Fall 1428 0 0.0994398 0.1085657 1.1529185 yes
Louisiana Summer 1855 0 0.3347709 0.5529719 2.6690359 yes
Louisiana Fall 1721 0 0.1865195 0.1924564 0.9155669 yes
MS Bight Summer 669 0 0.1898356 0.2170336 0.9896145 yes
MS Bight Fall 627 0 0.1052632 0.0768747 0.3133009 yes
Florida Summer 1570 0 0.0159236 0.0133319 0.1728732 yes
Florida Fall 966 0 0.0051760 0.0014906 0.0206892 no

Seasonal Catch Plot

Survey Year Season Stations Missing Obs % Occurrence Mean Catch SD Overdispersed
2000 Summer 247 0 0.1862348 0.2433493 1.0107420 yes
2000 Fall 244 0 0.0614754 0.0422881 0.2591299 yes
2001 Summer 172 0 0.2383721 0.9058880 3.8750995 yes
2001 Fall 244 0 0.1024590 0.0547825 0.2016932 no
2002 Summer 258 0 0.2829457 0.4726460 1.9025609 yes
2002 Fall 256 0 0.1484375 0.1389847 0.6233534 yes
2003 Summer 202 0 0.3613861 0.4879959 1.2586940 yes
2003 Fall 276 0 0.1014493 0.2062844 1.3333858 yes
2004 Summer 247 0 0.2348178 0.3531264 1.3490575 yes
2004 Fall 193 0 0.1243523 0.1636476 0.7790789 yes
2005 Summer 178 0 0.3258427 1.2727272 6.7005425 yes
2005 Fall 252 0 0.2896825 0.3510905 1.3841155 yes
2006 Summer 233 0 0.3433476 0.4557953 1.6027673 yes
2006 Fall 160 0 0.1062500 0.0568084 0.2036120 no
2007 Summer 179 0 0.2793296 0.2644754 0.7826726 yes
2007 Fall 222 0 0.2162162 0.4575232 2.7767255 yes
2008 Summer 287 0 0.1254355 0.0771652 0.2744329 no
2008 Fall 309 0 0.1747573 0.1000198 0.3058358 no
2009 Summer 536 0 0.2369403 0.2210027 0.7005416 yes
2009 Fall 439 0 0.0592255 0.0311017 0.1442607 no
2010 Summer 385 0 0.2025974 0.2037817 0.6380942 yes
2010 Fall 314 0 0.1019108 0.0641468 0.2577660 yes
2011 Summer 329 0 0.2401216 0.2478884 0.6765975 yes
2011 Fall 220 0 0.1454545 0.2086794 1.0527617 yes
2012 Summer 391 0 0.1023018 0.0670658 0.2382140 no
2012 Fall 198 0 0.0707071 0.0448467 0.2265906 yes
2013 Summer 312 0 0.1121795 0.0706708 0.3087307 yes
2013 Fall 191 0 0.0261780 0.0156520 0.1350885 yes
2014 Summer 363 0 0.1212121 0.1713822 1.6492954 yes
2014 Fall 321 0 0.1028037 0.0711885 0.2949376 yes
2015 Summer 375 0 0.1813333 0.1653163 0.5749717 yes
2015 Fall 321 0 0.0747664 0.0637213 0.4888268 yes
2016 Summer 353 0 0.1643059 0.1479499 0.5227903 yes
2016 Fall 194 0 0.1030928 0.0621916 0.2923462 yes
2017 Summer 322 0 0.1987578 0.2661089 0.8896509 yes
2017 Fall 281 0 0.0498221 0.0216505 0.1216030 no
2018 Summer 284 0 0.1232394 0.0910192 0.3813359 yes
2018 Fall 107 0 0.1121495 0.0470648 0.1589276 no

Candidate Models

Formulation AIC Delta AIC
no interactions 13649.41 143.030608
year * region 13506.38 0.000000
year * season 13547.85 41.477763
region * season 13650.10 143.728943
all interactions 13510.21 3.830144

Catch per Hectare Plot